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Nontwist non-Hamiltonian systems

“…As usually found in the literature, scenario (i) is observed for rotation numbers with even denominators, whereas scenario (ii) applies to odd denominators. Nevertheless, as demonstrated in [11], scenario (i) is not expected in the absence of symmetries [scenario (ii) is then observed for both even and odd cases] (see, e.g., [19]). As final remarks we mention that the shearless torus on the diagonal also exhibits the collision scenario [type (i)].…”

“…Around the shearless torus different nontwist phenomena were discovered in Hamiltonian systems, e.g., separatrix reconnections and island chains collisions [7], manifold reconnections of hyperbolic points in the chaotic regime [13], meandering [14], and the fractality of the shearless torus at criticality [8,15,16]. These phenomena were observed in area preserving maps [7,8,17] and Hamiltonian flows with one and a half [12,18] and two [19] degrees of freedom and they typically have a strong impact in transport properties of the system. In this paper we show the existence of the nontwist phenomena in time-reversible non-Hamiltonian maps and flows.…”

Interference of robust tori on the resonance overlap

“…These are the isochronous resonances. The non-twist condition for Hamiltonian flux [4,5] is naturally manifested in the rotation number or in the safety factor in the context of plasma physics [6]. The safety factor, in this case, presents a nonmonotonic profile which can trigger multiple instability modes [7].…”